34+65-x+32=x2-13

Solution for 34+65-x+32=x2-13 equation:

34+65-x+32=x2-13

We move all terms to the left:

34+65-x+32-(x2-13)=0

We add all the numbers together, and all the variables

-(+x^2-13)-x+34+65+32=0

We add all the numbers together, and all the variables

-(+x^2-13)-1x+131=0

We get rid of parentheses

-x^2-1x+13+131=0

We add all the numbers together, and all the variables

-1x^2-1x+144=0

a = -1; b = -1; c = +144;
Δ = b2-4ac
Δ = -12-4·(-1)·144
Δ = 577
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{577}}{2*-1}=\frac{1-\sqrt{577}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{577}}{2*-1}=\frac{1+\sqrt{577}}{-2}
$